Inset Square From a Rectangular Face
There isn't direct way to inset a face without taking into account proportions of the parent face, however you can use addon to workaround that.

After inset use Circle option of the LoopTools addon (addon comes with Blender by default; addon should be activated in User prefs). Operator will likely rotate the face, you will need to rotate it back so that it fits parent face (if the resulting face is oriented unevenly in the global space you should rotate it around its normal to avoid distortions).



If in 2.79 this will be in W menu > LoopTools. In 2.8 it depends on preferences you set for selection mouse button (right or left). By default, it should be in the Right click menu.

Note that Circle operator isn't generally designed for equalizing proportions of faces rather it does what its name suggests - converts selection to circle. As the face in this case consists of 4 vertices it works as expected. If you were insetting Ngon this way would created a circle.